/*
 * A pedagogical implementation of A5/1.
 *
 * Copyright (C) 1998-1999: Marc Briceno, Ian Goldberg, and David Wagner
 *
 * The source code below is optimized for instructional value and clarity.
 * Performance will be terrible, but that's not the point.
 * The algorithm is written in the C programming language to avoid ambiguities
 * inherent to the English language. Complain to the 9th Circuit of Appeals
 * if you have a problem with that.
 *
 * This software may be export-controlled by US law.
 *
 * This software is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.
 * Copyright remains the authors' and as such any Copyright notices in
 * the code are not to be removed.
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 * 
 * The license and distribution terms for any publicly available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution license
 * [including the GNU Public License.]
 *
 * Background: The Global System for Mobile communications is the most widely
 * deployed cellular telephony system in the world. GSM makes use of
 * four core cryptographic algorithms, neither of which has been published by
 * the GSM MOU. This failure to subject the algorithms to public review is all  
 * the more puzzling given that over 100 million GSM
 * subscribers are expected to rely on the claimed security of the system.
 *
 * The four core GSM algorithms are:
 * A3		authentication algorithm
 * A5/1		"strong" over-the-air voice-privacy algorithm
 * A5/2		"weak" over-the-air voice-privacy algorithm
 * A8		voice-privacy key generation algorithm
 *
 * In April of 1998, our group showed that COMP128, the algorithm used by the
 * overwhelming majority of GSM providers for both A3 and A8
 * functionality was fatally flawed and allowed for cloning of GSM mobile
 * phones.
 * Furthermore, we demonstrated that all A8 implementations we could locate,
 * including the few that did not use COMP128 for key generation, had been
 * deliberately weakened by reducing the keyspace from 64 bits to 54 bits.
 * The remaining 10 bits are simply set to zero!
 *
 * See http://www.scard.org/gsm for additional information.
 *
 * The question so far unanswered is if A5/1, the "stronger" of the two
 * widely deployed voice-privacy algorithm is at least as strong as the
 * key. Meaning: "Does A5/1 have a work factor of at least 54 bits"?
 * Absent a publicly available A5/1 reference implementation, this question
 * could not be answered. We hope that our reference implementation below,
 * which has been verified against official A5/1 test vectors, will provide
 * the cryptographic community with the base on which to construct the
 * answer to this important question.
 *
 * Initial indications about the strength of A5/1 are not encouraging.
 * A variant of A5, while not A5/1 itself, has been estimated to have a
 * work factor of well below 54 bits. See http://jya.com/crack-a5.htm for
 * background information and references.
 * 
 * With COMP128 broken and A5/1 published below, we will now turn our attention
 * to A5/2. The latter has been acknowledged by the GSM community to have
 * been specifically designed by intelligence agencies for lack of security.
 *
 * We hope to publish A5/2 later this year.
 *
 * -- Marc Briceno	<marc@scard.org>
 *    Voice:		+1 (925) 798-4042
 *
 */


#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <string.h>
#include <math.h>

/* Masks for the three shift registers */
#define R1MASK	0x07FFFF /* 19 bits, numbered 0..18 */
#define R2MASK	0x3FFFFF /* 22 bits, numbered 0..21 */
#define R3MASK	0x7FFFFF /* 23 bits, numbered 0..22 */

/* Middle bit of each of the three shift registers, for clock control */
#define R1MID	0x000100 /* bit 8 */
#define R2MID	0x000400 /* bit 10 */
#define R3MID	0x000400 /* bit 10 */

/* Feedback taps, for clocking the shift registers.
 * These correspond to the primitive polynomials
 * x^19 + x^5 + x^2 + x + 1, x^22 + x + 1,
 * and x^23 + x^15 + x^2 + x + 1. */
#define R1TAPS	0x072000 /* bits 18,17,16,13 */
#define R2TAPS	0x300000 /* bits 21,20 */
#define R3TAPS	0x700080 /* bits 22,21,20,7 */

/* Output taps, for output generation */
#define R1OUT	0x040000 /* bit 18 (the high bit) */
#define R2OUT	0x200000 /* bit 21 (the high bit) */
#define R3OUT	0x400000 /* bit 22 (the high bit) */

typedef unsigned char byte;
typedef unsigned long word;
typedef word bit;

/* Calculate the parity of a 32-bit word, i.e. the sum of its bits modulo 2 */
bit parity(word x) {
  //	x ^= x>>32;
	x ^= x>>16;
	x ^= x>>8;
	x ^= x>>4;
	x ^= x>>2;
	x ^= x>>1;
	return x&1;
}

/* Clock one shift register */
word clockone(word reg, word mask, word taps) {
	word t = reg & taps;
	reg = (reg << 1) & mask;
	reg |= parity(t);
	return reg;
}

/* The three shift registers.  They're in global variables to make the code
 * easier to understand.
 * A better implementation would not use global variables. */
word R1, R2, R3;

/* Look at the middle bits of R1,R2,R3, take a vote, and
 * return the majority value of those 3 bits. */
bit majority() {
	int sum;
	sum = ((R1&R1MID) >> 8) + ((R2&R2MID) >> 10) + ((R3&R3MID) >> 10);
	if (sum >= 2)
		return 1;
	else
		return 0;
}

/* Clock two or three of R1,R2,R3, with clock control
 * according to their middle bits.
 * Specifically, we clock Ri whenever Ri's middle bit
 * agrees with the majority value of the three middle bits.*/
inline void clock() {
	bit maj = majority();
	if (((R1&R1MID)!=0) == maj)
		R1 = clockone(R1, R1MASK, R1TAPS);
	if (((R2&R2MID)!=0) == maj)
		R2 = clockone(R2, R2MASK, R2TAPS);
	if (((R3&R3MID)!=0) == maj)
		R3 = clockone(R3, R3MASK, R3TAPS);
}

/* Generate an output bit from the current state.
 * You grab a bit from each register via the output generation taps;
 * then you XOR the resulting three bits. */
bit getbit() {
  //	return parity(R1&R1OUT)^parity(R2&R2OUT)^parity(R3&R3OUT);
  return ((R1&R1OUT) >> 18) ^ ((R2&R2OUT) >> 21) ^ ((R3&R3OUT) >> 22);
}

inline word calculate_link (word input, word count) {
  word result;
  int i;

  input ^= count ^ (count << 23) ^ (count << (22 + 23));

  R1 = (input >> (22 + 23)) & R1MASK;
  R2 = (input >> 23) & R2MASK;
  R3 = input & R3MASK;

  result = getbit();
  for(i=1;i<64;i++) {
    clock();
    result = (result << 1)| getbit();
  }
  return result;
}
  

int main(int argc, char* argv[]) {
  int i,j;
  word current;

  sscanf(argv[1], "%16lx", &current);

  for(i=pow(2,21);i>0;i--) {
    current = calculate_link(current, i);
  }

  printf("%16.16lx\n", current);
  return 0;
}